Abstract
Reconstructing the evolutionary relationships among the orders of eutherian mammals entails the identification of a single true phylogenetic tree out of approximately 1019 possible ones. The morphological and paleontological legacy to the field consists of numerous contradictory trees that are mostly devoid of binary resolution. With the introduction of molecular methodologies, several superordinal relationships have been identified, and in several instances a complete taxonomic revision was indicated. In this review, I present a summary of the phylogenetic affinities of the eutherian orders as revealed by molecular studies, and outline the differences between the molecular phylogenetic schemes and the phylogenetic trees produced through the use of morphological data. Questions of monophyly or paraphyly of the eutherian orders are also discussed. It is estimated that all but 109 of the 1019 possible phylogenetic trees have been ruled out by molecular analysis, and that DNA and protein sequences with their potential to supply millions of phylogenetically useful characters will resolve the phylogeny of the orders of mammals into a consistently bifurcating tree in the not-so-distant future.